In maximizing the directivity of large circular arrays with many parallel dipoles, it is necessary to consider the mutual coupling effects of the currents in the many dipoles. An application of the method of moments in the numerical solution will require the inversion of large matrices and lead to computational difficulties. In this paper these difficulties are alleviated by employing two techniques. First, the simultaneous integral equations are converted into matrix equations by the three-term approximation. Dipole subdivisions are not required, thus greatly reducing the size of the matrices. Second, a rotational operator is defined, with which a unitary transformation is applied to the array matrix. The inversion of the array matrix can then be effected by a straightforward matrix-multiplication process. Typical numerical results on maximum obtainable directivity and on the radiation pattern of an optimized circular array of 30 parallel dipoles are presented.